Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 14 views

    Mi1016 GK20201

    Uploaded by

    Đức Anh Lê
    This document contains a mid-term exam for Calculus 1 with 8 questions. The exam is for Course ID MI1016 and lasts 60 minutes. Questions cover determining domains, limits, derivatives, integrals, and asymptotes of various functions as well as proving trigonometric inequalities.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Mi1016 GK20201

    Uploaded by

    Đức Anh Lê
    14 views1 page
    This document contains a mid-term exam for Calculus 1 with 8 questions. The exam is for Course ID MI1016 and lasts 60 minutes. Questions cover determining domains, limits, derivatives, integrals, and asymptotes of various functions as well as proving trigonometric inequalities.

    Original Description:

    Original Title

    MI1016_GK20201

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    This document contains a mid-term exam for Calculus 1 with 8 questions. The exam is for Course ID MI1016 and lasts 60 minutes. Questions cover determining domains, limits, derivatives, integrals, and asymptotes of various functions as well as proving trigonometric inequalities.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    14 views1 page

    Mi1016 GK20201

    Uploaded by

    Đức Anh Lê
    This document contains a mid-term exam for Calculus 1 with 8 questions. The exam is for Course ID MI1016 and lasts 60 minutes. Questions cover determining domains, limits, derivatives, integrals, and asymptotes of various functions as well as proving trigonometric inequalities.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 1

    Code 1 School of Applied Mathematics and Informatics Code 2 School of Applied Mathematics and Informatics

    CALCULUS 1: MID-TERM EXAM - 20201 CALCULUS 1: MID-TERM EXAM - 20201


    Course ID: MI1016. Time: 60 minutes. Course ID: MI1016. Time: 60 minutes.
    Note: Documents are not allowed. Note: Documents are not allowed.

    Question 1. Determine the domain of Question 1. Determine the domain of

    y = arccos(e x ). y = arcsin(e x ).
     x  x
    2 − 1 3 − 1
    if x 6= 0, if x 6= 0,
    Question 2. For what value of a is f ( x ) = x Question 2. For what value of a is f ( x ) = x
    a if x = 0 a if x = 0
    continuous on R. continuous on R.
    Question 3. Evaluate the following limits Question 3. Evaluate the following limits
    3x − arctan(3x )  x 2x − arctan(2x )  x
    a) lim b) lim sin 1x + cos 2x . a) lim 2 1
    b) lim sin x + cos x .
    x →0 x3 x →∞ x →0 x3 x →∞

    Question 4. Determine the local extreme values of Question 4. Determine the local extreme values of
    q q
    f ( x ) = 3 x ( x − 2)2 . f ( x ) = 3 x ( x + 2)2 .

    Question 5. Find the nth derivative of the function Question 5. Find the nth derivative of the function
    x x
    f (x) = . f (x) = .
    ( x − 1)( x + 2) ( x + 1)( x + 2)

    Question 6. Evaluate the following integrals Question 6. Evaluate the following integrals
    R ex R ex
    b) ln( x2 + 4)dx. b) ln( x2 + 1)dx.
    R R
    a) 2x
    dx a) 2x
    dx
    e +1 e +4
    Question 7. Determine the asymptotes of the curve Question 7. Determine the asymptotes of the curve

    1 1
    y = x arccot . y = x arccot .
    x x

    Question 8. Prove that Question 8. Prove that


    x x
    tan x < √ for all x ∈ (0; 1). tan x < √ for all x ∈ (0; 1).
    1− x2 1 − x2

    You might also like